解答 - 几何数列

要找到系列的通用形式，将第一项：$$a=500$$ 和公比：$$r=-0.6$$ 插入几何级数的公式：

$$a_1=500$$

$$a_2=a_1·r^{n-1}=500\cdot -{0.6}^{2-1}=500\cdot -{0.6}^1=500\cdot -0.6=-300$$

$$a_3=a_1·r^{n-1}=500\cdot -{0.6}^{3-1}=500\cdot -{0.6}^2=500\cdot 0.36=180$$

$$a_4=a_1·r^{n-1}=500\cdot -{0.6}^{4-1}=500\cdot -{0.6}^3=500\cdot -0.21599999999999997=-107.99999999999999$$

$$a_5=a_1·r^{n-1}=500\cdot -{0.6}^{5-1}=500\cdot -{0.6}^4=500\cdot 0.1296=64.8$$

$$a_6=a_1·r^{n-1}=500\cdot -{0.6}^{6-1}=500\cdot -{0.6}^5=500\cdot -0.07775999999999998=-38.87999999999999$$

$$a_7=a_1·r^{n-1}=500\cdot -{0.6}^{7-1}=500\cdot -{0.6}^6=500\cdot 0.04665599999999999=23.327999999999996$$

$$a_8=a_1·r^{n-1}=500\cdot -{0.6}^{8-1}=500\cdot -{0.6}^7=500\cdot -0.027993599999999993=-13.996799999999997$$

$$a_9=a_1·r^{n-1}=500\cdot -{0.6}^{9-1}=500\cdot -{0.6}^8=500\cdot 0.016796159999999994=8.398079999999997$$

$$a_{10}=a_1·r^{n-1}=500\cdot -{0.6}^{10-1}=500\cdot -{0.6}^9=500\cdot -0.010077695999999997=-5.038847999999999$$